Programul Seminarului de Cercetare de Analiză Geometrică. Anul universitar Seminarul se ţine in fiecare joi între orele 9-12.

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1 Programul Seminarului de Cercetare de Analiză Geometrică Anul universitar Seminarul se ţine in fiecare joi între orele 9-12 Sala A313 Membrii: Brigitte Breckner Lisei Hannelore Ildiko Mezei Alexandru Kristály Csaba Varga Radu Peter Csaba Farkas Andrea Molnar Orsolya Vas I. Funcţii cu variaţie mărginită II. Funcţii cu variaţie mărginită generalizată III. Formula ariei ş co-ariei IV.Inegalităţi izoperimetrice Bibliografie. 1. E. Giusti, Minimal surfaces and Functions of Bounded Variation, Birkhäuser, Selecta of Elliott H. Lieb, Inequalities, Edited by M. Loss and M. B. Ruskai, Springer, Vladimir Maz ya, Sobolev space, Springer, M. Amar, G. Bellettini, A notion of total variations depending on a metric with discontinuous coefficients, Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994),

2 V. Simetrizări convexe VI. Simetrizări anizotrope VII. Inegalitatea lui Pólya-Szegő in cazul simetrizărilor convexe şi anizotrope VIII. Cazul de egalitate în inegalitatea lui Pólya-Szegő Bibliografie: 1. Jean VAN SCHAFTINGEN, Anisotropic symmetrization, Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 4, A. Alvino, V. Ferone, G. Trombetti, P.-L. Lions, Convex symmetrizations, A.I.H.P., Section C, 14(1997), S. Kesevan, Symmetrzation & Applications, World Scientific, L. Fanghuan, Y. Xiaoping, Geometric measures theory, Science Press, F. Morgan, Geometric Measures Theory, Academic Press, A. Ferone, R. Volpicelli, Convex rearrangement: Equality case in the Pólya-Szegő Inequality, Calc. Var. 21(2004), L. Esposito, C. Trombetti, Convex symmetrization and Pólya-Szegő inequality, Nonlinear Anal. 56(2004), IX. Ecuaţii eliptice şi rearanjări X. Operatorul lui Finsler-Laplace si aplicatii XI. Teoreme de comparare a lui Talenti XII. Inegalitatea lui Faber - Krahn XIII. Inegalitatea lui Szegő - Weinberger XIV. Teorema lui Chiti XV. Inegalitatea lui Payne-Pólya Weinberger XVI. Problema supradeterminata anisotropa (Overdetermined anisotropic problems) XVII. Inegalitati de tip Caffarelli-Kohn-Nirenberg pe varietati Finsler cu curbura Ricci nenegativa: rezultate de rigiditate. Bibliografie 1. A. Cianchi, P. Salani, Overdetermined anisotropic elliptic problems. Math. Ann. 345 (2009), no. 4, V. Ferone, B. Kawohl, Remarks on a Finsler-Laplacian, Proc. AMS, 137(2009), M. Belloni, V. Ferone, B. Kawohl, Isoperimetric inequalities, Wulff shape and related questions for strongly nonlinear elliptic operators, J. Appl. Math. Phys. (ZAMP) 54 (2003), p B. Kawohl, K.I. Fragala and F. Gazzola: Existence and nonexistence results for anisotropic quasilinear elliptic equations, Ann Inst. H. Poincaré 21 (2004), p

3 5. S. Kesevan, Symmetrzation & Applications, World Scientific, A. Kristaly, Anisotropic Singular Phenomena in the Presence of Asymmetric Minkowski Norms, preprint (2012). 7. A. Kristaly, Caffarelli-Kohn-Nirenberg inequalities on Finsler manifolds with nonnegative Ricci curvature, preprint (2012). 8. M. Ashbaugh, R. Benguria, A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions, Annals of Math., 135(1992), M. Ashbaugh, R. Benguria, Proof of the Payne-Pólya Weinberger conjecture, Bull. AMS, 25(1991), XVIII. Elemente de teoria punctului critic XIX. Simetrizări si principii minimax XX. Aproximarea simetrizărilor şi simetria punctelor critice Bibliografie. 1. J. VAN SCHAFTINGEN and M. WILLEM, Set transformations, symmetrizations and isoperimetric inequalities, in Nonlinear analysis and applications to physical sciences,springer Italia, Milan, 2004, Jean VAN SCHAFTINGEN, Symmetrization and minimax principles, Commun. Contemp. Math. 7 (2005), no. 4, Jean VAN SCHAFTINGEN, Approximation of symmetrizations and symmetry of critical points, Topol. Methods Nonlinear Anal. 28 (2006), no. 1, M. Willem, Minimax theorems, Birkhäuser, 1996, XXI. Spaţii de funcţii pe spatii metrice XXII. Rearanjarea cu două puncte in spaţii metrice XXIII. Sisteme de rearanjări XXIV. Dezintegrarea măsurilor si rearanjări Steiner şi Schwarz XXV. Grupuri Heisenberg si spaţii Sobolev pe grupuri Heisenberg XXVI. Scufundari compacte pe grupuri Heisenberg XXVII. Rezultate de multiplicitate pe grupuri Heisenberg XXVIII. Rearajanjări pe grupuri Heisenberg XXIX. Teorema ariei, co-ariei şi teorema lui Pansu XXX. Inegalităţi izoperimetrice în grupuri Heisenberg Bibliografie 1. Z. Balogh, A. Kristaly, Lions-type compactness and Rubik actions on the Heisenberg group, Calc. Var. (2012), in press.

4 2. L. Capogna, D. Danielli, S.D. Pauls, J.T. Tyson, An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem, Birkhauser, D. Prandi, Rearrangement in metric space, Ph.D. these, Universite a degli Studi di Padova, Anno Academico 2009/ R. Monti, Rearrengement in metric space and in the Heisenberg groups, Prepint, 2010.

5 The plan of the research seminary on Geometric Analysis Academic year Every Thursday, Hours 9-12 Room A313 Members: Brigitte Breckner Lisei Hannelore Ildiko Mezei Alexandru Kristály Csaba Varga Radu Peter Csaba Farkas Andrea Molnar Orsolya Vas I. Functions of bounded variation II. Generalized functions of bounded variation III. The area and co-area formula IV. Isoperimetric inequalities 1. E. Giusti, Minimal surfaces and Functions of Bounded Variation, Birkhäuser, Selecta of Elliott H. Lieb, Inequalities, Edited by M. Loss and M. B. Ruskai, Springer, Vladimir Maz ya, Sobolev space, Springer, 1985.

6 4. M. Amar, G. Bellettini, A notion of total variations depending on a metric with discontinuous coefficients, Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994), V. Convex symmetrization VI. Anisotropic symmetrization VII. The Pólya-Szegő inequality in case of convex and anisotropic symmetrization VIII. Equality in the Pólya-Szegő inequality 1. Jean VAN SCHAFTINGEN, Anisotropic symmetrization, Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 4, A. Alvino, V. Ferone, G. Trombetti, P.-L. Lions, Convex symmetrizations, A.I.H.P., Section C, 14(1997), S. Kesevan, Symmetrzation & Applications, World Scientific, L. Fanghuan, Y. Xiaoping, Geometric measures theory, Science Press, F. Morgan, Geometric Measures Theory, Academic Press, A. Ferone, R. Volpicelli, Convex rearrangement: Equality case in the Pólya-Szegő Inequality, Calc. Var. 21(2004), L. Esposito, C. Trombetti, Convex symmetrization and Pólya-Szegő inequality, Nonlinear Anal. 56(2004), IX. Elliptic equations and rearrangements X. The Finsler-Laplace operator and applications XI. Comparison theorems of Talenti XII. The Faber - Krahn inequality XIII. The Szegő - Weinberger inequality XIV. The theorem of Chiti XV. The Payne-Pólya Weinberger inequality XVI. Overdetermined anisotropic problems XVII. Caffarelli-Kohn-Nirenberg type inequalities on Finsler manifolds with nonnegative Ricci curvature: rigidity results

7 1. A. Cianchi, P. Salani, Overdetermined anisotropic elliptic problems. Math. Ann. 345 (2009), no. 4, V. Ferone, B. Kawohl, Remarks on a Finsler-Laplacian, Proc. AMS, 137(2009), M. Belloni, V. Ferone, B. Kawohl, Isoperimetric inequalities, Wulff shape and related questions for strongly nonlinear elliptic operators, J. Appl. Math. Phys. (ZAMP) 54 (2003), p B. Kawohl, K.I. Fragala and F. Gazzola: Existence and nonexistence results for anisotropic quasilinear elliptic equations, Ann Inst. H. Poincaré 21 (2004), p S. Kesevan, Symmetrzation & Applications, World Scientific, A. Kristaly, Anisotropic Singular Phenomena in the Presence of Asymmetric Minkowski Norms, preprint (2012). 7. A. Kristaly, Caffarelli-Kohn-Nirenberg inequalities on Finsler manifolds with nonnegative Ricci curvature, preprint (2012). 8. M. Ashbaugh, R. Benguria, A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions, Annals of Math., 135(1992), M. Ashbaugh, R. Benguria, Proof of the Payne-Pólya Weinberger conjecture, Bull. AMS, 25(1991), XVIII. Elements of critical point theory XIX. Symmetrizations and minimax principles XX. Approximation of symmetrizations and symmetry of critical points 1. J. VAN SCHAFTINGEN and M. WILLEM, Set transformations, symmetrizations and isoperimetric inequalities, in Nonlinear analysis and applications to physical sciences,springer Italia, Milan, 2004, Jean VAN SCHAFTINGEN, Symmetrization and minimax principles, Commun. Contemp. Math. 7 (2005), no. 4, Jean VAN SCHAFTINGEN, Approximation of symmetrizations and symmetry of critical points, Topol. Methods Nonlinear Anal. 28 (2006), no. 1, M. Willem, Minimax theorems, Birkhäuser, 1996, XXI. Functions spaces on metric spaces XXII. Rearrangement with two points in metric speces XXIII. Systems of rearrangements XXIV. Steiner and Schwarz rearrangements XXV. Heisenberg groups and Sobolev spaces on Heisenberg groups

8 XXVI. Compact embeddings in Heisenberg groups XXVII. Multiplicity results on Heisenberg groups XXVIII. Rearrangements in Heisenberg groups XXIX. The theorem of area, co-area and the theorem of Pansu XXX. Isoperimetric inequalities in Heisenberg groups 1. Z. Balogh, A. Kristaly, Lions-type compactness and Rubik actions on the Heisenberg group, Calc. Var. (2012), in press. 2. L. Capogna, D. Danielli, S.D. Pauls, J.T. Tyson, An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem, Birkhauser, D. Prandi, Rearrangement in metric space, Ph.D. these, Universite a degli Studi di Padova, Anno Academico 2009/ R. Monti, Rearrangement in metric space and in the Heisenberg groups, Prepint, 2010.